Inclusive<i>S</i>-wave charmonium productions in<i>B</i>decays

Abstract

The inclusive S-wave charmonium production rates in B decays are considered using the Bodwin-Braaten-Lepage approach, including the relativistic corrections and the color-octet mechanism suggested as a possible solution to the \ensuremath{\psi}\ensuremath{'} puzzle at the Fermilab Tevatron. We first consider relativistic and radiative corrections to J/\ensuremath{\psi}\ensuremath{\rightarrow}${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ and J/\ensuremath{\psi}\ensuremath{\rightarrow} light hadrons (LH's), in order to determine two nonperturbative parameters, 〈J/\ensuremath{\psi}\ensuremath{\Vert}${\mathit{O}}_{1}$${(}^{3}$${\mathit{S}}_{1}$)\ensuremath{\Vert}J/\ensuremath{\psi}〉, 〈J/\ensuremath{\psi}\ensuremath{\Vert}${\mathit{P}}_{1}$${(}^{3}$${\mathit{S}}_{1}$)\ensuremath{\Vert}J/\ensuremath{\psi}〉, in the factorization formulas for these decays. Using these two matrix elements and including the color-octet cc\ifmmode\bar\else\textasciimacron\fi{}${(}^{3}$${\mathit{S}}_{1}$) state contribution, we get a moderate increase in the decay rates for B decays into J/\ensuremath{\psi} (or \ensuremath{\psi}\ensuremath{'})+X. Our results B(B\ensuremath{\rightarrow}J/\ensuremath{\psi} (or \ensuremath{\psi}\ensuremath{'})+X)=0.58 (0.23)% for ${\mathit{M}}_{\mathit{b}}$=5.3 GeV get closer to the recent CLEO data. As a by-product, we prefer a larger decay rate for ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$\ensuremath{\rightarrow}LH compared to the present data. \textcopyright{} 1996 The American Physical Society.